A semi-relativistic treatment of spinless particles subject to the nuclear Woods-Saxon potential

TL;DR

This paper develops an approximate analytical method to solve the semi-relativistic two-body spinless Salpeter equation with the Woods-Saxon potential, providing energy eigenvalues and wave functions for arbitrary angular momentum states.

Contribution

It introduces a Pekeris approximation-based systematic solution for the spinless Salpeter equation with Woods-Saxon potential, covering arbitrary l-states and special cases.

Findings

Derived semi-relativistic bound-state energy eigenvalues.

Obtained wave functions for the system.

Analyzed special cases including Schrödinger-Woods-Saxon and s-wave solutions.

Abstract

By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter (SS) equation with the Woods-Saxon interaction potential for arbitrary -state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied: the approximated Schr\"odinger-Woods-Saxon problem for arbitrary l -state and the exact s-wave (l=0).